Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1297
... norm is the norm of the pair [ f , T1f ] as an element of the graph of T1 ( 7 ) . Now T1 ( 7 ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( T1 ( t ) ) is complete in the norm f1 . Since the two additional terms in [ f2 ...
... norm is the norm of the pair [ f , T1f ] as an element of the graph of T1 ( 7 ) . Now T1 ( 7 ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( T1 ( t ) ) is complete in the norm f1 . Since the two additional terms in [ f2 ...
Page 1431
... norm of D ( T , ( t ' ) ) coincides with the closure of D ( To ( t ' ) ) in the norm of D ( T1 ( t ) ) . 2 1 Let D1 and D2 be the closures of D ( To ( 7 ′ ) ) in the norms of D ( T1 ( t ' ) ) and D ( T1 ( 7 ) ) respectively . By step ...
... norm of D ( T , ( t ' ) ) coincides with the closure of D ( To ( t ' ) ) in the norm of D ( T1 ( t ) ) . 2 1 Let D1 and D2 be the closures of D ( To ( 7 ′ ) ) in the norms of D ( T1 ( t ' ) ) and D ( T1 ( 7 ) ) respectively . By step ...
Page 1699
... norm of HP ) ( L ) of a sequence { g } of functions in Co ( L ) . Putting ĝ , ( x ) = 0 for a in C - L , it follows from Definition 3.15 that Fe is the limit in the norm of HP ) ( C ) of the sequence { g ; } of elements of Co ( C ) ...
... norm of HP ) ( L ) of a sequence { g } of functions in Co ( L ) . Putting ĝ , ( x ) = 0 for a in C - L , it follows from Definition 3.15 that Fe is the limit in the norm of HP ) ( C ) of the sequence { g ; } of elements of Co ( C ) ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero